IMPLICIT AND FORMAL USES OF A FLAT METRIC IN GENERAL RELATIVITY
The meaning of functions of the Riemannian coordinates and their relation to measurements are investigated. It is shown how symmetries of a Riemannian space-time describable by groups of motions may be given physical interpretation in terms of fiat space-time concepts. The linear first integrals of the differential equations of motion of a test particle in a curved space-time are interpreted in terms of flat space-time counterparts. Analysis of the symmetries admitted by the Friedmann-Lemaitre space-time for an open cosmological model shows that they have the same structure as the homogeneous Lorentz group of a flat space-time expressed in a properly chosen coordinate system, in which the components of the flat metric tensor are functions of time. This relationship is interpreted with respect to possible inertial properties of the cosmological model. Einstein's linearized field theory for weak gravitational fields is analyzed. It is shown how the nat space-time implicit in Einstein's treatment can be given formal recognition in a more general manner. Einstein's linearized weak-field theory is extended so that nearly flat Riemannian space-times cam be represented in terms of deviations from flat space-times expressed in any coordinate system. It is hypothesized that a flat metric can formally be introduced into general relativity as a concomitant second metric, which is interpreted as characterizing an operationally Euclidean observer. The association of a particular flat metric with a particular curved metric is shown to be equivalent to relating the Riemannian observables to the measurements of a particular observer. It is shown that symmetries admitted by the curved space- time aid in the proper matching of curved and flat space-times. Kohler's two metric principle of equivalence and Rosen's variable mass treatment are considered. The formulation of covariant conservation laws for the gravitational field are briefly discussed. (M.P.G.)
- Research Organization:
- Originating Research Org. not identified
- NSA Number:
- NSA-18-008946
- OSTI ID:
- 4091474
- Resource Relation:
- Other Information: Thesis. Orig. Receipt Date: 31-DEC-64
- Country of Publication:
- Country unknown/Code not available
- Language:
- English
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